In this paper, we propose the regression-based packet loss concealment (PLC) for digital speech transmission by using deep neural networks (DNNs) with a multiple-layer deep architecture. For the DNN training, log-power spectra and phases are employed as features in the input layer for the large training set, which ensures non-linear mapping the frames from the last correctly received frame to the missing frame. Once the training is accomplished by the restricted Boltzmann machine (RBM)-based pre-training to initialize the DNN, minimum mean square error (MMSE)-based fine tuning is then performed based on the back-propagation algorithm. In the reconstruction stage, the trained DNN model is fed with the features of the previous frames in order to estimate the log-power spectra and phases of the missing frames. Reconstruction is further improved by using the cross-fading technique to mitigate discontinuity between the reconstruction signal and good frame signal in the time-domain. To demonstrate the performance of the proposed algorithm, hidden Markov model (HMM)-based PLC algorithm and the PLC algorithm standardized in adaptive multi-rate wideband (AMR-WB) Appendix I were used for comparison. The experimental results show that the proposed approach provides better speech quality and speech recognition accuracy than the conventional approaches.